Simulations networked activity using dynamics-based constraints on reusable network component

ABSTRACT

Techniques for simulating networks using dynamics-based constraints are disclosed.

CROSS-REFERENCE TO RELATED APPLICATION

The present application is a continuation of, and claims the benefit ofand priority to, U.S. Ser. No. 16/443,968, filed Jun. 18, 2019, theentire contents of which are incorporated herein by reference for allpurposes.

FIELD

Methods and systems disclosed herein relate generally to generatingdynamics-based constraints on activity of reusable network components innetwork simulations.

BACKGROUND

The development of accurate simulations and models can facilitategeneration of testable and focused hypotheses. Some simulations ofsystems are constructed based on bottom-up knowledge. Specifically, theactivity and interaction of particular low-level components may be knownin some contexts, and the simulation may be generated to replicate theselow-level activities and interactions. When such low-level operation canbe simulated for many components, high-level activity of a network ofthe components can be simulated. Some simulations are constructed usinga top-down configuration. Specifically, a simulation can be constructedto perform in accordance with high-level activity with more flexibilityafforded to low-level components.

One value of simulations is to be able to generate predictions as to howa given new set of inputs or simulation alterations would affectoperation (e.g., output and/or activity) of the overall system and/or ofindividual components of the system. This information can be used todetermine how to respond to a given system state by further adjustingthe system in a particular manner to maintain high performance of thesystem.

The value of the simulations may be particularly high for biologicalsimulations. For example, the simulation may be used to identify how agiven biological deficit may cascade to affect other processes.Identifying a therapeutic to target one of these downstream effects maybe an effective treatment option. However, such use cases rely uponsimulations that accurately model low-level component function,high-level activity, dynamics across levels, and component interactions.

SUMMARY

In some embodiments, a computer-implemented method is provided. A set ofreactions representative of activity of a biological network isidentified. Each reaction identifying stoichiometry is indicative ofrelative quantities of metabolites being consumed and produced by thereaction. Based on the set of reactions, a metabolite is identified thatis reused across cycles of at least one reaction. A constraint on aquantity of the metabolite is defined based on one or morecharacteristics of the reuse of the metabolite across cycles of the atleast one reaction. A simulation is executed using the set of reactionsand the constraint. Execution of the simulation generates one or moresimulation outputs.

In some instances, the method further includes identifying a use rateindicative of a quantity of the cycles of the at least one reactionperformed per unit of time; and identifying a per-cycle duration of theat least one reaction; where the one or more characteristics of thereuse of the metabolite include the use rate and the per-cycle duration.In some instances, the at least one reaction includes a set ofreactions, where a first reaction of the set of reactions consumes themetabolite, and a later reaction of the set of reactions releases themetabolite. In some instances, the method further includes determiningthat the metabolite is further reused across other cycles of another atleast one reaction; where the constraint on the quantity of themetabolite is defined further based on one or more other characteristicsof the reuse of the metabolite across other cycles of the other at leastone reaction. In some instances, the constraint is defined to indicatethat the quantity of the metabolite is to remain to be at least equal toa sum of multiple product values, the multiple product values including:a first product of a first use rate and a first duration correspondingto the at least one reaction; and a second product of a second use rateand a second duration corresponding to the other at least one reaction.In some instances, the biological network is a cell, and the metaboliteis a cofactor, enzyme or ribosome. In some instances, executing thesimulation includes identifying, for each reaction of the set ofreactions, a flux of the reaction based on an objective function that isdefined based on the stoichiometries of the set of reactions. In someinstances, the one or more simulation outputs include time-course dataindicating dynamics of at least part of the network. In some instances,executing the simulation includes using linear programming.

Some embodiments of the present disclosure include a system includingone or more data processors. In some embodiments, the system includes anon-transitory computer readable storage medium containing instructionswhich, when executed on the one or more data processors, cause the oneor more data processors to perform part or all of one or more methodsand/or part or all of one or more processes disclosed herein. Someembodiments of the present disclosure include a computer-program producttangibly embodied in a non-transitory machine-readable storage medium,including instructions configured to cause one or more data processorsto perform part or all of one or more methods and/or part or all of oneor more processes disclosed herein.

The terms and expressions which have been employed are used as terms ofdescription and not of limitation, and there is no intention in the useof such terms and expressions of excluding any equivalents of thefeatures shown and described or portions thereof, but it is recognizedthat various modifications are possible within the scope of theinvention claimed. Thus, it should be understood that although thepresent invention has been specifically disclosed by embodiments andoptional features, modification and variation of the concepts hereindisclosed may be resorted to by those skilled in the art, and that suchmodifications and variations are considered to be within the scope ofthis invention as defined by the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure is described in conjunction with the appendedfigures:

FIG. 1 shows an interaction system for configuring and using asimulation to facilitate subsequent experiment configurations accordingto some embodiments of the invention;

FIG. 2 shows a representation of modules representing distinctbiological functions according to an embodiment of the invention;

FIG. 3 shows a simulation controller that dynamically integrates resultsgenerated by different types of models to simulate higher-level statesand reactions according to some embodiments of the invention;

FIG. 4 shows a process for dynamically synthesizing results generated bymultiple simulators to simulate higher-level results according to anembodiment of the invention;

FIG. 5 shows a module-specific simulation controller to simulate statesand reactions according to some embodiments of the invention;

FIG. 6 shows a process for using a simulator to generate metabolitetime-course data according to an embodiment of the invention;

FIG. 7 shows a process for simulating network activity according to anembodiment of the invention;

FIG. 8 shows a representation of reaction series in which a non-consumedcomponent is used;

FIG. 9 shows a partial representation of physiological states of areaction according to an embodiment of the invention;

FIG. 10 shows examples of dynamics of components of a simulated network;and

FIG. 11 shows examples of dynamics of components of a simulated networkwhen constraints on reusable components are used.

In the appended figures, similar components and/or features can have thesame reference label. Further, various components of the same type canbe distinguished by following the reference label by a dash and a secondlabel that distinguishes among the similar components. If only the firstreference label is used in the specification, the description isapplicable to any one of the similar components having the same firstreference label irrespective of the second reference label.

DETAILED DESCRIPTION

The ensuing description provides preferred exemplary embodiments only,and is not intended to limit the scope, applicability or configurationof the disclosure. Rather, the ensuing description of the preferredexemplary embodiments will provide those skilled in the art with anenabling description for implementing various embodiments. It isunderstood that various changes may be made in the function andarrangement of elements without departing from the spirit and scope asset forth in the appended claims.

Specific details are given in the following description to provide athorough understanding of the embodiments. However, it will beunderstood that the embodiments may be practiced without these specificdetails. For example, circuits, systems, networks, processes, and othercomponents may be shown as components in block diagram form in order notto obscure the embodiments in unnecessary detail. In other instances,well-known circuits, processes, algorithms, structures, and techniquesmay be shown without unnecessary detail in order to avoid obscuring theembodiments.

Also, it is noted that individual embodiments may be described as aprocess which is depicted as a flowchart, a flow diagram, a data flowdiagram, a structure diagram, or a block diagram. Although a flowchartor diagram may describe the operations as a sequential process, many ofthe operations may be performed in parallel or concurrently. Inaddition, the order of the operations may be re-arranged. A process isterminated when its operations are completed, but could have additionalsteps not included in a figure. A process may correspond to a method, afunction, a procedure, a subroutine, a subprogram, etc. When a processcorresponds to a function, its termination may correspond to a return ofthe function to the calling function or the main function.

In some instances, techniques are disclosed for simulating activitywithin a network. For example, the simulation may simulate reactionsoccurring within a cell. The simulation may use (for example)mechanistic-based models, structural models, constraint-based modelsand/or reaction-based models. In some instances, the cell is representedby one or more modules, and a model (e.g., representing one or morereactions) is assigned to each module. At each time step, for eachmodule, input data (e.g., identifying levels of various metabolites) isretrieved and processed by the assigned model to produce output data. Atleast part of the input data may be retrieved from a cross-module datastructure. Corresponding elements of the output data can be synthesizedacross modules and used to update the cross-module data structure. Thus,the simulation can be used to determine how metabolite levels andreaction prevalence change in time given a particular cellconfiguration. For example, the simulation can be used to determine howa particular mutation affects a growth rate of a cell and whichreactions and/or metabolites are constraining the growth.

In some instances, a model that is used in the simulation (e.g., acrossthe entire simulation or for one or more modules) is configured tobalance compounds, such that a quantity of each given compound that isconsumed by a set of reactions is equal to a quantity of the givencompound that is produced by the set of reactions. Each reaction mayhave fixed stoichiometry, such that the simulation is configured tosecure this balance by identifying relative ratios and/or fluxes atwhich the reactions are performed.

However, when a compound is recycled instead of being consumed, asimulation may detect the non-consumed compound as being consistentlybalanced regardless of a flux of the corresponding reaction(s). Thus, asimulation may (for example) produce a solution that would require moreof these non-consumed compounds than were available, which could lead tounphysiological results.

One approach to address this issue is to add a constraint thatconstrains a level of a consumed compound or a flux of a reaction basedon a level of the non-consumed compound. However, in this instance, ifthe constraint limits an objective of the simulation, the limit would beascribed to a limit of the non-consumed compound. This may notaccurately represent the physiological circumstances that actually limitthe objective. For example, suppose that an objective is set to maximizegrowth and that a reaction is defined that requires a non-consumedcompound and that transforms a reactant compound to a product compoundrequired for growth. Further consider a constraint that is defined thatprevents performance of the reaction or that limits a quantity of thereactant compound when the non-consumed compound is absent or limited.Results of the simulation may then indicate that growth was stunted as aresult of the non-consumed compound be absent or of low levels, ratherthan indicating that the growth was stunted as a result of the productcompound being absent or present at low levels.

In some embodiments, a simulation is configured that includes aconstraint that relates a level of the non-consumed compound to dynamicsof the reaction or series of reactions that require the non-consumedcompound. The dynamics pertain both to a flux of the reaction or seriesof reactions indicating a rate at which the reaction or series ofreactions is simulated as occurring and a duration of part or all of thereaction or series of reactions. For example, the duration may include aduration of a full reaction or full series of reactions or a partthereof that involves the non-consumed compound. That is, the durationmay correspond to a sequestration duration during which a giveniteration of a reaction or series of reactions is using the non-consumedcompound such that it is unavailable to be used in another iteration ofthe reaction or series of reactions.

While a given non-consumed compound may be repeatedly used acrossdifferent iterations of a reaction or series of reactions, sequestrationdurations limit this repeated use. For example, if a sequestrationduration was half of a time-step duration, the non-consumed compoundcould contribute to, at most, two reactions or series of reactions pertime step. Thus, simulating performance of ten iterations of thereaction or series of reactions per time step would require a presenceof at least ten non-consumed compounds. Thus, the constraint can requirethat an availability, quantity or count of the non-consumed compound begreater than or equal to a product of the sequestration duration and aflux of the associated reaction or series of reactions that indicates aquantity of the reaction or series of reactions occurring per unit time.

In some instances, a non-consumed compound may be used in multiple typesof reactions and/or series of reactions. An availability of thenon-consumed compound may then be affected by sequestration durations ofthe multiple types of reactions and/or series of reactions and on thefluxes of the multiple types of reactions and/or series of reactions.Accordingly, a constraint may be applied that indicates that anavailability, quantity or count of the non-consumed compound is to begreater than or equal to a sum of reaction-specific orreaction-series-specific products of a respective sequestration durationand flux.

In some instances, the constraint is implemented as a hard constraint,such that each solution that is identified by the simulation is requiredto and necessarily conforms with the constraint. Thus, if execution ofthe simulation does not identify any solution that conforms with theconstraint (and each other constraint), the simulation terminates (e.g.,reflecting cell death). In some instances, rather than enforcing theabove-defined relative equation as a constraint.

FIG. 1 shows an interaction system 100 for configuring instances orversions of a model and using a simulation to facilitate subsequentexperiment configurations (e.g., simulation of a biological system'sresponse to a new demand) according to various embodiments. Eachinstance of the models may have a combination of modules, perturbations(such as knockouts), and may be built using a particular set ofexperimental data. In order to facilitate the configuring of a model(e.g., a biological system) and simulate an outcome of the model, theinteraction system 100 can include one or more components, each of whichcan include (for example) one or more servers, one or more computersand/or one or more mobile devices. In some instances, two or more of thecomponents can be included in a same server, same server system, samecomputer, etc. Interaction system 100 can include one or more networks(e.g., a wired network, a wireless network, the Internet, a local areanetwork, a wide area network, a short-range network, etc.), such thateach component in the interaction system 100 can communicate with one ormore other components in the interaction system 100.

Interaction system 100 can include a simulation controller 105 thatdefines, generates, updates and/or executes each of one or moresimulations. A simulation can be configured to simulate dynamicprogression through states, a time-evolved state of a model of abiological system and/or a steady state based on an iterativemodule-based assessment. It will be appreciated that identifying asteady-state and/or balanced solution for a module at a given time stepneed not indicate that a steady-state and/or balanced solution has been,can be or will be identified for the model in general (e.g., asmetabolites produced and/or consumed at one module may further beproduced and/or consumed at another module that need not be configuredfor balancing fluxes).

A given model can be used to generate and run any number of simulations.Differing initial conditions and/or differing automatically generatedvalues in stochastic portions of the simulation (e.g., generated using apseudo-random number generation technique, a stochastic pull from adistribution, etc.) can result in different output results of differentsimulations. The biological system model can be made up of one or moremodules, and during a simulation run, each module is run independentlyand passes results back up to the biological system model level. Morespecifically, the biological system (e.g., a whole cell) may be modeledin accordance with a coordinated operation of multiple modules thatrepresent structure(s) and/or function(s) of the biological system. Eachmodule may be defined to execute independently, except that a shared setof state values (e.g., a state vector) maintained at the biologicalsystem model level may be used and accessed by multiple modules at eachtime point.

In some instances, each module of the biological system is configured toadvance across iterations (e.g., time points) using one or morephysiological and/or physics-based models (e.g., flux balance analysis(FBA), template synthesis, bulk-mass flow analysis, constantnon-specific degradation, empirical analysis, etc.). The module-specificiteration processing can further be based on one or more module-specificstate values (as determined based on an initial definition for aninitial iteration processing or a result of a previous iterationprocessing for a subsequent iteration processing). The module-specificiteration processing can further be based on one or more parametersdefined for the module that are fixed and/or static across iterationsacross iterations.

Simulation controller 105 can generate simulation configurations usingone or more inputs received from a user device 110. For example,simulation controller 105 may generate an interface (or may at leastpartly define specifications for an interface) that is to be availedand/or transmitted to user device 110 and to include input fieldsconfigured to receive inputs that correspond to a selection of (forexample) one or more modules to be used for a given biological systemmodel, a model type to be used for each of the one or more modules, oneor more parameters that are to be effected by a given module's model andused during execution, and/or one or more initial state-valuedefinitions that are to be used by a given module's model and usedduring execution. In some instances, the interface identifies a defaultvalue for each of one, more or all parameters of the model and for eachof one, more or all of the initial-state values of the model and isconfigured to receive a modification to a subset or all of theparameters and/or initial-state values for which a default value wasidentified. In some instances, modifying a default initial-state valueand/or parameter can correspond to a perturbation of performance of acorresponding module and/or the biological system.

As another example, the interface may further or alternatively beconfigured to receive an input that corresponds to a selection of one ormore default modules and a selection of a model type to be used for eachof one or more modules. For example, the interface may include one ormore modules (as shown in FIG. 2 ) representing distinct biologicalfunctions in a biological system model, and for each module: a name ofthe module, a default model type for the module and an option configuredto receive a selection of another model type for the module (e.g., thatidentifies one or more other model types that can be selected for themodule).

Default structure of a simulation (e.g., corresponding to defaultmodules, default parameters, default initial-state values and/or defaultmodel selections) can be determined based on detected internal orexternal content and/or based on lab results (e.g., results fromphysical experiments). The content can include (for example) online,remote and/or local content that is collected by a content bot 115.Content bot 115 can (for example) include a crawler that performs afocused crawling and/or focused browsing (for example) the Internet, apart of the Internet, one or more pre-identified websites, a remote(e.g., cloud-based) storage system, a part of a remote storage system, alocal storage system and/or a part of a local storage system. Thecrawling can be performed in accordance with one or more crawlingpolicies and/or one or more queries that corresponds to one or moremodules and/or models (e.g., where each query includes a variable name,representation or description and/or a cellular-function name,representation or description).

The lab results can be received from a wet-lab value detection system120, which can be configured to trigger performance of one or moreinvestigations (e.g., physical experiments) to detect and/or measuredata corresponding to an initial-state value and/or data correspondingto a characteristic or parameter of a biological system. Wet-labvalue-detection system 120 can transmit one or more results of theinvestigation(s) back to simulation controller 105, which may thereafterdetermine and/or define a default initial-state value or parameter or apossible modification thereof based on the result(s).

Interaction system 100 further includes a simulation validator 125,which can be configured to validate performance of a simulation. Thevalidation may be performed based on pre-identified indications as tohow a biological system functions normally and/or given one or moreperturbations. Such indications can be defined based on contentcollected from content bot 115 and/or results from wet-labvalue-detection system 120. The data used to validate the simulation mayinclude (for example) one or more balanced values, one or more valuesindicative of cell dynamics, one or more steady-state values, one ormore intermediate values and/or one or more time-course statistics.Simulation validator 125 may return a performance result that includes(for example) a number, category, cluster or binary indicator tosimulation controller 105. Simulation controller 105 may use the resultto determine (for example) whether a given simulation configuration issuitable for use (e.g., in which case it may be selectable in aninterface).

After a simulation is configured with definitions and/or selections ofmodules, module-specific models, parameters and/or initial-state values,simulation controller 105 can execute the simulation (e.g., in responseto receiving an instruction from user device 110 to execute thesimulation). The simulation execution can produce one or more simulationresults, which may include (for example) one or more balanced values,kinetic values, etc. For example, the simulation can identify a solutionfor a set of reaction-corresponding stoichiometric equations usinglinear algebra, such that production and consumption of metabolitesrepresented in the equations is balanced. Notably, this balance may bespecific to a given module and need not be achieved for all metabolitesproduced or consumed by reactions for a given module (e.g., as anon-zero net production or consumption of one or more boundarymetabolites may be predefined and/or a target result for a module).Simulation controller 105 can transmit the results (e.g., via aninterface) to user device 110.

In some instances, the results can be used to trigger and/or define asubsequent experiment. For example, simulation controller 105 maydetermine whether a given predefined condition is satisfied based on theresults and, if so, may transmit simulation-specific data (e.g.,indicating one or more initial-state values, parameters, mutationscorresponding to simulation definitions, etc.) to an experimental system130. The transmission may be indicative of and/or include an instructionto perform an experiment that corresponds to the simulation.

As another example, upon receiving simulation results from simulationcontroller 105, user device 110 can present an interface that includessome or all of the results and an input component configured to receiveinput corresponding to an instruction to perform an experiment thatcorresponds to the simulation. Upon receiving a selection at the inputcomponent, user device 110 may transmit data corresponding to thesimulation to experimental system 130. After performing a requestedexperiment, experimental system 130 may return one or more results tosimulation controller 105 and/or user device 110.

FIG. 2 shows an illustrative representation of given biological systemmodel 200. The overall modeling strategy includes partitioning thebiological system model 200 into modules that can be modeled separately,using a methodology and level of detail appropriate to and/or selectedfor each module. The partitioning and level of detail for each modulecan be selected based on (for example) the experiments or simulationsthat are to be run by the model (e.g., the questions trying to be solvedby the model). The selection may be made by the modeler and/or computingsystem (e.g., the interaction system 100 described with respect to FIG.1 ). For example, a user working through an interface of an integrateddevelopment environment, a script, and/or an automated system may beimplemented to select one or more modules and select a model type to beused for each of one or more modules to ultimately generate thebiological system model 200. Additionally or alternatively, thepartitioning can be customized and depend on an assessment of thebiological functions defined for the initial high-level data set. Forexample, a separate module may be defined to represent each of thefollowing biological functions: core metabolism 205, membrane synthesis210, cell-wall synthesis 215, DNA replication 220, transcription 225,transcription regulation 230, translation 235, RNA salvage (not shown),protein and RNA maturation, protein salvage (not shown), transmembranetransport 240 (including electron chain, oxidative phosphorylation,redox, and pH interconversion activity 245), signal transduction (notshown), stress response and growth rate regulation 250, cell division,chemotaxis (not shown), and cell-cell signaling (not shown).

Biological system model 200 can include at least one module that handlescore metabolism 205. One possible core metabolic module uses an FBAmodel, which takes its general shape from standalone FBA, but includesmodifications that account for interactions of the core metabolic modulewith other modules. Each of one, more or all other modules may havetheir own production and consumption of some of the same moleculeswithin the FBA network, as described in further detail herein. However,as should be understood to those of ordinary skill in the art, an FBAmodel does not have to be incorporated into the overall biologicalsystem model 200 in order for every simulation to work. Instead, varioustypes of models can be used for the modules (e.g., core metabolism 205,membrane synthesis 210, cell-wall synthesis 215, etc.) so long as thetype of models can be configured to read values from the state vectorand return a list of changes that should be made to the state vector.

For one exemplary instantiation of biological system model 200, coremetabolism 205, membrane synthesis 210, and cell-wall synthesis 215 maybe encompassed as a single FBA problem, whereas DNA replication 220,transcription 225, transcription regulation 230, and translation 235 maybe isolated from the rest of the metabolic network. Meanwhile,transcription 225 and translation 235 may use a template synthesismodel, and DNA replication 220 may use a bulk mass-flow model.Transcription regulation 230 may be empirical and static. Optionally,RNA salvage may be modeled using constant non-specific degradation,polymerized DNA, RNA, and protein levels may be determined by theintrinsic rates of the processes that produce them, and the remainder ofthe components are provided as inputs or parameters of the model.

For another exemplary instantiation of biological system model 200, coremetabolism 205 may be encompassed as a single FBA problem. The balanceof internal metabolite pools and the supply of building blocks for otherprocesses may be maintained by core metabolism 205. DNA replication 220,transcription 225, transcription regulation 230, and translation 235 maythen be isolated from the rest of the metabolic network. Membranebiosynthesis 210 and cell-wall synthesis 215 may be modeled bysubstrate- and catalyst-driven kinetics. Import and export rates and allexchange with the environment may be driven by the kinetics of membranetransport. Transcription 225 and translation 235 may use a templatesynthesis model, and DNA replication 220 may use a bulk mass-flow model.Transcription regulation 230 may be empirical and static. Optionally,RNA salvage may be modeled using representations of constantnon-specific degradation, while polymerized DNA, RNA, and protein levelsmay be determined by the intrinsic rates of the processes that producethem, and the remainder of the components for the biological system canbe provided as inputs or parameters of the model.

For another exemplary instantiation of biological system model 200, coremetabolism 205 may be encompassed as an FBA problem, whereas one or moreof membrane synthesis 210, cell-wall synthesis 215, DNA replication 220,transcription 225, transcription regulation 230, and translation 235 canbe isolated from the rest of the metabolic network. The balance ofinternal metabolite pools and the supply of building blocks for otherprocesses may be maintained by core metabolism 205. Membranebiosynthesis 210 and cell-wall synthesis 215 may be modeled by substrateand catalyst driven kinetics. Import and export rates, and all exchangewith the environment may be driven by the kinetics of membranetransport. Redox balance, pH, and chemiosmotic gradients may bemaintained explicitly. DNA replication 220, transcription 225 andtranslation 235 may use models based on initiation, elongation, andtermination, Transcription regulation 230 may be pattern driven. Stressresponse and growth rate regulation 250 may be modeled using feedbackcontrol mechanisms. Optionally, RNA salvage may be modeled usingconstant non-specific degradation, while polymerized DNA, RNA, andprotein levels may be determined by the intrinsic rates of the processesthat produce them, and the remainder of the components for thebiological system can be provided as inputs or parameters of the model.

While the biological system model 200 has been described at some lengthand with some particularity with respect to several described modules,combinations of modules, and simulation techniques, it is not intendedthat the biological system model 200 be limited to any such particularmodule configuration or particular embodiment. Instead, it should beunderstood that the described embodiments are provided as examples ofmodules, combinations of modules, and simulation techniques, and themodules, combinations of modules, and simulation techniques are to beconstrued with the broadest sense to include variations of modules,combinations of modules, and simulation techniques listed above, as wellas other modules, combinations of modules, and simulation techniquesconfigurations that could be constructed using a methodology and levelof detail appropriate to each module and the biological system model200.

FIG. 3 shows a simulation controller 300 that dynamically integratesresults generated by different types of models configured by anintegrated development environment (e.g., the interaction system 100described with respect to FIG. 1 ) to simulate higher-level states andreactions of a biological system model (e.g., biological system model200 as described with respect to FIG. 2 ) according to variousembodiments. A partitioner 305 that can identify one or more modules topotentially use for a simulation. In some instances, the modules areidentified to correspond to distinct biological functions orphysiological processes within a biological system model. Nonetheless,at least one module (e.g., a core module) may address in more detail orcover a larger set of biological functions (e.g., correspond to a corelevel of physiology across the biological system such as generalmetabolism of the biological system), whereas at least one other module(e.g., a non-core module) may address in less detail or cover a smallerset biological function (e.g., correspond to transcription and/ortranslation).

A module-specific simulation assignor 310 may assign, to each module, asimulation type. The simulation type can be selected from amongst one ormore types that are associated with the module and/or correspondingphysiological process. The one or more types may differ with regard to(for example) a degree of detail to which a physiological process ismodeled and/or how the process is modeled. For example, the one or moretypes may include a simulation using a metabolism-integrated model(e.g., in which specific end products are added to an objective functionof a metabolism-based model), substrate- and/or catalyst-drive modelusing kinetic parameters and reactions, and/or higher-order structuremodel. A structure for each simulation type (e.g., that indicates howthe simulation is to be performed and/or program code) is included in asimulator structure data store 315. Simulator structure data store 315can further store an association between each simulation type and one ormore modules for which the simulation type is associated and ispermitted for selection for use.

A module-specific simulator controller 320 can identify, for eachmodule, one or more simulation parameters and an input data set. Thesimulation parameters may be retrieved from a local data store (e.g., asimulator parameters data store 325) or from a remote source. Each ofone or more of the simulation parameters may have been identified basedon (for example) user input, a data-fitting technique and/or remotecontent. The parameter(s), once selected, may be fixed across time-stepiterations.

At an initial time step, the input data set can include one or moreinitial input values, which may be retrieved from a local data store(e.g., an initial input data store 330) or from a remote source. Each ofone or more of the initial input values may have been identified basedon (for example) user input, a data-fitting technique and/or remotecontent. With respect to each subsequent time step, the input data setcan include (for example) one or more results from a previous iterationof the module and/or one or more high-level results (e.g., cumulative orintegrated results) generated from a previous iteration of themulti-module simulation. For example, a module-specific results datastore 335 may store each of one, more or all results generated by theassigned simulation for each of one, more or all past time steps, and atleast one of the stored results associated with a preceding time step(e.g., most recent time step) can be retrieved.

Upon identifying the input data set and parameters, module-specificsimulator controller 320 can run the simulation assigned to the module.Execution of module-specific simulations may be performed concurrently,in parallel and/or using different resources (e.g., differentprocessors, different memory and/or different devices). Results of thesimulation run can be stored in module-specific results data store 335.

After results have been generated for each module, a cross-module resultsynthesizor 340 can access the module-specific results (from one or moremodule-specific results data stores or direct data availing) andsynthesize the results to update high-level data such as a state vector(e.g., stored in a high-level metabolite data store 345). For example, aset of results generated by different modules but relating to a samevariable may be identified. The results may be integrated by (forexample) summing variable changes as indicated across the results (e.g.,potentially with the implementation of one or more caps pertaining to asummed change or to a value of a variable after the summed change iseffected). In some instances, a hierarchy is used, such that a resultfrom one module (if available or if another condition is met) is to beexclusively used and a result from another module is to otherwise beused.

Upon synthesizing the results, a time-step incrementor 350 can incrementa time step to a next time step so long as the simulation has notcompleted. It may be determined that the simulation is complete when(for example) processing for a predefined number of time steps has beenperformed, a particular result is detected (e.g., indicating that atarget cell growth has occurred or that a cell has died) or steady statehas been reached (e.g., as indicated by values for one or morepredefined types of results differing by less than a predefinedthreshold amount across time steps). When the time step is incremented,module-specific simulator controller 320 can, for each module, collect anew input data set and run the assigned simulation. When the simulationis complete, an output can be generated to include one or moremodule-specific results, some or all high-level data and/or processedversions thereof. For example, the output may include time-course datafor each of one or more metabolites, growth of the biological systemover a time period (e.g., as identified by a ratio of availabilityvalues of one or more particular metabolites at a final time step ascompared to availability values at an initial time step) and/or a growthrate. The output can be transmitted to another device (e.g., to bepresented using a browser or other application) and/or presentedlocally.

Multi-module simulation controller 300 can also include a perturbationimplementor 355. Perturbation implementor 355 can facilitatepresentation of an interface on a user device. The interface canidentify various types of perturbations (e.g., mutations). Perturbationimplementor 355 may facilitate the presentation by transmitting data(e.g., HTTP data) to a user device, such that the interface can bepresented online. Perturbation implementor 355 can detect a selectionthat corresponds to a particular perturbation and can send an indicationto module-specific simulator controller 320. Module-specific simulatorcontroller 320 can use functional gene data to determine how themutation affects one or more metabolites and/or one or more simulatedprocesses. A structure of a simulator, one or more simulator parametersand/or one or more initial-input values may then be adjusted inaccordance was the perturbation's effects. Thus, multi-module simulationcontroller 300 can generate output that is indicative of how theperturbation affects (for example) physiological processes and/or growthof the biological system.

FIG. 4 shows a process 400 for dynamically synthesizing resultsgenerated by multiple simulators to simulate higher-level resultsaccording to various embodiments. In some embodiments, the processesdepicted in process 400 are implemented by the interaction system 100 ofFIG. 1 , and discussed with respect to the simulation controller 300 ofFIG. 4 . Process 400 begins at block 405 at which an initial high-leveldata set is defined for a biological system model. The initialhigh-level data set can identify (for example) variables, which may bereferred to as the state of the biological system model or the state ofthe simulation, and these variables may be structured as a datastructure (e.g., a state vector) and updated throughout a simulationrun. In some instances, the variables include an initial availability ofeach of a set of molecules such as metabolites. The initial availabilitymay be defined based on (for example) a default value, user input, dataextracted from content (e.g., online content, remote content or localcontent that pertains to the molecules), etc. In some instances, theinitial availability is determined based on whether any perturbation wasidentified (e.g., via user input) for a given simulation. If aperturbation was identified, the initial availability may be determinedbased on a particular perturbation that was identified and by using (forexample) a look-up table to determine for which molecule(s) theperturbation affects an availability value and characteristics of sucheffect.

At block 410, a biological system model (e.g., a whole cell model) ispartitioned into multiple modules. The partitioning can depend onmetabolite dependencies and/or biological-functioning assessment. Forexample, a separate module may be defined to represent each of thefollowing biological functions: core metabolism, membrane synthesis,cell-wall synthesis, DNA replication, transcription, transcriptionregulation, translation, RNA salvage, protein and RNA maturation,protein salvage, transmembrane transport (including electron chain,oxidative phosphorylation, redox, and pH interconversion activity),signal transduction, stress response and growth rate regulation (SOS),cell division, chemotaxis, and cell-cell signaling, as discussed infurther detail with respect to FIG. 2 . In some instances, two or moreof these functions may be represented in a core module that models cellcomposition and growth using a single model. Particular cellularfunctioning need not be explicitly modeled and instead dynamics of endproducts of the particular cellular functioning may be modeled. Forexample, a core module may use a flux-based analysis or a simulationtechnique as described herein (e.g., in relation to FIG. 5 or FIG. 6 ).

In some instances, the partitioning may be performed based on user inputand/or one or more default configurations. For example, an interface maybe presented that identifies each potential separate module (e.g., aninterface may be presented via simulation controller 105 as describedwith respect to FIG. 1 ). A default configuration may be to integratethe module into a core module (e.g., a core metabolism module) unless acontrary input is received or to perform a simulation using modelingspecific to the module unless a contrary input is received. For example,an interface may be configured to receive one or more selections ofmodules that are to be excluded from a core module and to then integrateeach other module into the core module.

At block 415, for each module, one or more simulation techniques areassigned to the module. A simulation technique may include a model type.In some instances, a simulation technique that is assigned to a coremodule includes a flux-based analysis or other simulation technique, asdescribed herein. In some instances, a simulation technique includes amechanistic model, a kinetic model, a partial kinetic model, asubstrate- and/or catalyst-driven model, and/or a structural model. Thesimulation technique may be assigned based on (for example) user inputand/or one or more predefined default selections. For example, for eachnon-core module, a default selection may be predefined that representsparticular functioning of the module, and for each core module, adefault selection may be predefined that simulates dynamics ofmetabolites across a simulated time period. An interface may identify,for each module, the default selection along with one or more othersimulation techniques that are associated with the module (e.g., withthe association(s) being based on stored data and/or a predefinedconfiguration). User input may then indicate that an alternativesimulation technique is to be used for one or more modules.

At block 420, for each module, a simulator is configured by settingparameters and variables. The parameters (e.g., numeric values) maycorrespond to inputs to be used in the simulation technique assigned tothe module and that are not changed across time steps of the simulation.The particular parameters may be determined based on (for example)stored data, content, a communication from another system and/or userinput. The one or more module-specific or cross-module variables (e.g.,identifying an initial availability of one or more metabolites) maycorrespond to inputs to be used in the simulation technique assigned tothe module and may be changed across time steps of the simulation. Forexample, a parameter may be determined for a simulator that sets aminimum viable pH in the cytoplasm (below which the cell dies), and avariable may be identified that describes a current pH in the cytoplasm.The variable (current pH) might change throughout the simulation;however, the parameter (the minimum possible pH) would not change andremains fixed. An initial value of the pH variable may be identified,e.g., the value at the start of the simulation may be set in step 405 orif it is module specific then it may be set in step 420, and like theminimum pH parameter this would be used as an input into the simulation.The values of variables and parameters are both inputs, but thedistinction is that variables can change from their initial values, andparameters are fixed throughout the simulation run.

At block 425, a time step is incremented, which can initially begin agiven simulation. At block 430, for each module, module-specific inputdata is defined at least in part on the high-level data. Morespecifically, a high-level data structure may identify, for each of aset of molecules (e.g., metabolites), an availability value. Eachavailability value may initially be set to an initial availabilityvalue, which may thereafter be updated based on processing results fromeach module that relates to the molecule. For a given module, at eachtime step, a current availability value can be retrieved from the datastructure for each molecule that pertains to the simulation techniqueassigned to the module. The module-specific input data may furtherinclude one or more lower-level values that are independent fromprocessing of any other module. For example, one or more variables mayonly pertain to processing of a given module, such that themodule-specific input data may further include an initial value or pastoutput value that particularly and exclusively relates to the module.

At block 435, for each module, the configured simulator assigned to themodule is run using the module-specific input data to generate one ormore module-specific results. The one or more module-specific resultsmay include (for example) one or more updated molecule availabilityvalues and/or a change in one or more availability values relative tocorresponding values in the input data.

At block 440, results can be synthesized across modules. The synthesismay include summing differences across modules. For example, if a firstmodule's results indicate that an availability of a given molecule is tobe increased by 5 units and a second module's results indicate that anavailability of the given metabolite is to be decreased by 3 units, anet change may be calculated as being an increase in 2 units. The netchange can then be added to a corresponding availability value for themolecule that was used for the processing associated with the currenttime step and returned as a list of changes that should be made to thestate vector. One or more limits may be applied to a change (e.g., todisallow changes across time steps that exceed a predefined threshold)and/or to a value (e.g., to disallow negative availability values andinstead set the value to zero).

At block 445, the high-level data set is updated based on thesynthesized results. The update can include adding data to a datastructure such as a state vector from which one or more modules retrievehigh-level data. The added data can include the synthesized results inassociation with an identifier of a current time step. Thus, the datastructure can retain data indicating how an availability of a metabolitechanged over time steps. It will be appreciated that alternatively theupdate can include replacing current high-level data with thesynthesized data.

At block 450, it is determined whether the simulation is complete. Thedetermination may be based on a number of time steps assessed, a degreeto which data (e.g., high-level data) is changing across time steps, adetermination as to whether a steady state has been reached, whether oneor more simulated biological events (e.g., cell division or cell death)have been detected, etc. If the simulation is not complete, process 400returns to block 425.

If the simulation is complete, process 400 continues to block 455, atwhich an output is generated. The output may include some or all of thehigh-level data and/or some or all of the module-specific results. Forexample, the output may include final availability values thatcorrespond to a set of metabolites and/or a time course that indicates achange in the availability of each of one or more metabolites over thesimulated time period. The output may be presented at a local deviceand/or transmitted to another device (e.g., for presentation).

FIG. 5 shows a module-specific simulation controller 200 to simulatestates and reactions of modules configured by an integrated developmentenvironment (e.g., the interaction system 100 described with respect toFIG. 1 ) according to various embodiments. A network constructor 505 canbe configured to use a model to simulate actions performed by a moduleof a biological system model (e.g., biological system model 200 asdescribed with respect to FIG. 2 ). In some instances, the model is fluxbalance analysis, and/or the model is configured to solve for updatedstate values based on a set of equations that represent concentrationchanges in the network (e.g., a metabolic network). As should beunderstood to those of ordinary skill in the art, a biological systemmodel such as a whole cell model does not have to include an FBA module.For example, from the framework described herein, biological processessuch as core metabolism may be modeled that is completely different fromFBA. In such an instance, part or all of the description and drawingspertaining to FIGS. 5 and 6 that is specific to FBA (e.g., objectivefunctions, constraints, and linear programming) may not be relevant tothat particular instantiation of the model or to simulations run withthat model. However, many of the components and techniques describedwith respect to FIGS. 5 and 6 could be applied to simulate states andreactions of modules implemented by other models. For example, anymodule can read values from the state vector and return an indication ofone or more changes that should be made to the state vector. The FBAmodule (if it's even present in a particular instantiation of the model)may read and return more values than any other model, but a modulemodeled with FBA need not be handled by the simulation controller 300any differently from other modules and/or models described herein.

Network constructor 505 can access a set of network data (e.g.,parameters and variables) stored in a network data store 510 to definethe model. Metabolite data 515 can identify each metabolite of ametabolome. As used herein, a “metabolite” is any substance that is aproduct of metabolic action or that is involved in a metabolic processincluding (for example) each compound input into a metabolic reaction,each compound produced by a metabolic reaction, each enzyme associatedwith a metabolic reaction, and each cofactor associated with a metabolicreaction. The metabolite data 515 may include for each metabolite (forexample) one or more of the following: the name of the metabolite, adescription, neutral formula, charged formula, charge, spatialcompartment of the biological system and/or module of the model, andidentifier such as PubChem ID. Further, metabolite data 515 can identifyan initial state value (e.g., an initial concentration and/or number ofdiscrete instances) for each metabolite.

Reaction data 520 can identify each reaction (e.g., each metabolicreaction) associated with the model. For example, a reaction canindicate that one or more first metabolites is transformed into one ormore second metabolites. The reaction need not identify one-to-onerelationships. For example, multiple metabolites may be defined asreaction inputs and/or multiple metabolites may be defined as reactionoutputs. The reaction data 520 may include for each reaction (forexample) one or more of the following: the name of the reaction, areaction description, the reaction formula, a gene-reaction association,genes, proteins, spatial compartment of the biological system and/ormodule of the model, and reaction direction. Further, the reaction data520 can identify, for each metabolite of the reaction, a quantity of themetabolite, which may reflect the relative input-output quantities ofthe involved metabolites. For example, a reaction may indicate that twofirst metabolites and one second metabolite are input into a reactionand that two third metabolites are outputs of the reaction. The reactiondata 520 can further identify an enzyme and/or cofactor that is requiredfor the reaction to occur.

Functional gene data 525 can identify genes and relationships betweengenes, proteins, and reactions, which combined provide a biochemically,genetically, and genomically structured knowledge base or matrix.Functional gene data 525 may include (for example) one or more of thefollowing: chromosome sequence data, the location, length, direction andessentiality of each gene, genomic sequence data, the organization andpromoter of transcription units, expression and degradation rate of eachRNA transcript, the specific folding and maturation pathway of RNA andprotein species, the subunit composition of each macromolecular complex,and the binding sites and footprint of DNA-binding proteins. Networkconstructor 505 can use functional gene data and the availability ofproteins encoded by those genes to update reaction constraints.

One exemplary technique by which genomic data can be associated withreaction data is evaluating Gene-Protein-Reaction expressions (GPR),which associate reactions with specific genes that triggered theformation of one or more specific proteins. Typically a GPR takes theform (Gene A AND Gene B) to indicate that the products of genes A and Bare protein sub-units that assemble to form a complete protein andtherefore the absence of either would result in deletion of thereaction. On the other hand, if the GPR is (Gene A OR Gene B) it impliesthat the products of genes A and B are isozymes (i.e., each of two ormore enzymes with identical function but different structure) andtherefore absence of one may not result in deletion of the reaction.Therefore, it is possible to evaluate the effect of single or multiplegene deletions by evaluation of the GPR as a Boolean expression. If theGPR evaluates to false, the reaction is constrained to zero in themodel.

A stoichiometry matrix controller 530 can use reaction data 520 togenerate a stoichiometry matrix 535. Along a first dimension of thematrix, different compounds (e.g., different metabolites) arerepresented. Along a second dimension of the matrix, different reactionsare represented. Thus, a given cell within the matrix relates to aparticular compound and a particular reaction. A value of that cell isset to 0 if the compound is not involved in the reaction, a positivevalue if the compound is one produced by the reaction and a negativevalue if the compound is one consumed by the reaction. The value itselfcorresponds to a coefficient of the reaction indicating a quantity ofthe compound that is produced or consumed relative to other compoundconsumption or production involved in the reaction.

Because frequently relatively few reactions correspond to a givencompound, stoichiometry matrix 535 can be a sparse stoichiometry matrix.Stoichiometry matrix 505 can be part of a set of model parameters(stored in a model-parameter data store 540) used to execute a module.

One or more modules may be configured to use linear programming 545 toidentify a set of compound quantities that correspond to balancingfluxes identified in reactions represented in stoichiometry matrix 535.Specifically, an equation can be defined whereby the product ofstoichiometry matrix 535 and a vector representing a quantity for eachof some of the compound quantities is set to zero. (It will beappreciated that the reactions may further include quantities for one ormore boundary metabolites, for which production and consumption need notbe balanced.) There are frequently multiple solutions to this problem.Therefore, an objective function is defined, and a particular solutionthat corresponds to a maximum or minimum objective function is selectedas the solution. The objective function can be defined as the productbetween a transposed vector of objective weights and a vectorrepresenting the quantity for each compound. Notably, the transposedvector may have a length that is equal to the first dimension ofstoichiometry matrix 535, given that multiple reactions may relate to asame compound.

The objective weights may be determined based on objectivespecifications 550, which may (for example) identify one or morereaction-produced compounds that are to be maximized. For example, theobjective weights can be of particular proportions of compounds thatcorrespond to biomass, such that producing compounds having thoseproportions corresponds to supporting growth of the biological system.

Each reaction may (but need not) be associated with one or more of a setof reaction constraints 555. A reaction constraint may (for example)constrain a flux through the reaction and/or enforce limits on thequantity of one or more compounds consumed by the reaction and/or one ormore compounds produced by the reaction.

In some instances, linear programming 545 uses stoichiometry matrix 535and reaction constraints 550 to identify multiple solutions, eachcomplying with the constraints. When multiple solutions are identified,objective specifications 550 can be used to select from amongst thepotential solutions. However, in some instances, no solution isidentified that complies with stoichiometry matrix 535 and reactionconstraints 555 and/or the only solution that complies with the matrixand constraints is not to proceed with any reaction.

A solution can include one in which, for each of a set of metabolites, aconsumption of the metabolite is equal to a production of themetabolite. That is not to say that this balance must be achieved foreach metabolite, as a set of reactions involve one or more “boundarymetabolites” for which this balance is not achieved. For example,glucose can be consumed at a given rate, and/or acetate can be producedat a given rate.

Reaction data 520 may further identify an objective function thatidentifies a target product (e.g., representing cell growth rate) thatis to be maximized. The objective function can identify particularratios of multiple reactant metabolites that must be available toproduce the product. Strictly enforcing the objective function mayresult in simulating no growth if a single metabolite is not produced.An alternative approach is to define one or more objective functionsconfigured such that production of each of multiple target reactantmetabolites that relate to the target product is to be maximized. Ahigher level whole-cell model can evaluate the production of multipletarget reactant metabolites to determine whether to and/or an extent towhich to simulate growth. For example, depending on which targetreactant metabolite(s) are not produced, the whole-cell model maynonetheless simulate cell growth, simulate cell growth at a reducedrate, simulate no growth, simulate unhealthy or impaired growth orsimulate cell death.

For example, a reaction space can be defined based on stoichiometrymatrix 535 and reaction constraints 555. The space may have as manydimensions as there are reactions. Each dimension can be restricted toinclude only integer values that extend along a range constrained by anyapplicable constraint in reaction constraints 555. A reaction spacesampler 560 can then determine, for each of some or all of the pointswithin the reaction space, a cumulative quantity of each metabolite thatwould be produced based on the associated reactions. Reaction spacesampler 560 can compare these quantities to those in the objectivevector (e.g., by determining an extent to which proportions of compoundsare consistent).

In these instances, a scoring function 565 can indicate how to scoreeach comparison. For example if proportions of each of two potentialsolutions differ from the objective proportions by 2, but one potentialsolution differs by 2 for a single compound and another by 1 for each oftwo compounds, scoring function 565 can be configured to differentiallyscore these instances. For example, different weights may be applied todifferent compounds, such that differences that affect a first compoundare more heavily penalized than differences that affect a secondcompound. As another example, scoring function 565 may indicate whethera score is to be calculated by (for example) summing allcompound-specific (e.g., weighted) differences, summing an absolutevalue of all compound-specific (e.g., weighted) differences, summing asquare of all compound-specific (e.g., weighted) differences, etc.Reaction space sampler 560 can then identify a solution as correspondingto reaction coefficients that are associated with a highest score acrossthe reaction space.

Network constructor 505 can receive results from each of linearprogramming 545 and/or reaction space sample 560. In some instances,linear programming 545 can further avail its results to reaction spacesample 560. When a balanced solution is identified by linear programming545, reaction space sampler 560 need not sample the reaction space andneed not avail reaction-space results to network constructor 505.

Network constructor 505 can identify a solution as corresponding to oneidentified by linear programming 545 when a balanced solution isidentified and as a highest-score potential solution identified byreaction space sampler 560 otherwise. The solution can then indicate thecompounds produced by and consumed by the reactions performed inaccordance with the solution-indicated flux. Network constructor 505 canupdate metabolite data 515 based on this production and consumption.

In some instances, a solution is identified for each of a set of timepoints rather than only identifying one final solution. The iterativetime-based approach may be useful when module-specific simulationcontroller 500 is but one of a set of simulation controllers andmetabolite data 515 is influenced by the performance of other modules.For example, metabolite data 515 may be shared across modules or may bedefined to be a copy of at least part of a cross-module metabolite dataset at each time point. The updates to the metabolites performed bynetwork constructor 505 may then be one of multiple updates. Forexample, an update by network constructor 505 may indicate that aquantity of a specific metabolite is to increase by four, while a resultfrom another module indicates that a quantity of the specific metaboliteis to decrease by two. Then the metabolite may change by a net of +2 forthe next time iteration.

A results interpreter 570 can generate one or more results based on theupdated metabolite data 515. For example, a result may characterize adegree of growth between an initial state and a steady state or finaltime point. The degree of growth may be determined based on a ratiobetween values of one or more metabolites at a current or final timepoint relative to corresponding values at an initial (or previous) timepoint. The one or more metabolites may correspond to (for example) thoseidentified in an objective function as corresponding to biomass growth.As another example, a result may characterize a time course of growth.For example, a result may identify a time required for metabolitechanges that correspond to a representation of a double in growth or atime constant determined based on a fit to values of one or more timeseries of metabolite values. The result(s) may be output (e.g., locallypresented or transmitted to a remote device, such as a user device). Theoutput can facilitate a presentation of an interface that indicates oneor more simulation characteristics (e.g., one or more default values interms of initial-state values or reaction data and/or one or moreeffected perturbations).

Operation of module-specific simulation controller 500 can be influencedby particular simulated perturbations of the whole cell. For example,each perturbation may correspond to a particular type of geneticmutation. The perturbation may have been identified based on detectinguser input (e.g., a selection and/or text input received via aninterface) that defines the perturbation. One exemplary type ofperturbation is a gene mutation. An effect of the perturbation may bedetermined based on functional gene data (e.g., to determine how anavailability of one or more metabolites is affected). High-levelmetabolite data, simulator parameters and/or high-level constraints maythen be accordingly set, constrained and/or defined based on theperturbation. This high-level perturbation can thus then influenceoperation of one or more lower level modules.

FIG. 6 shows a process 600 for using a simulator to generate metabolitetime-course data according to various embodiments. In some embodiments,the processes depicted in process 600 are implemented by the interactionsystem 100 of FIG. 1 , and discussed with respect to the module-specificsimulation controller 500 of FIG. 5 . Process 600 begins at block 605,at which a one or more modules within a metabolic network (e.g., of abiological system) are defined. The module(s) can be defined based onwhich parts of the network exhibit relative functional independenceand/or correspond to substantial independence in terms of biologicalactivity. In some instances, a default is to define each part of a cellas part of a core module unless a different module corresponding toparticular types of actions and/or cell components is defined.

At block 610, a set of reactions is defined for the network. In someinstances, the set of reactions are defined for the module (or eachmodule) that corresponds to the default model type. The set of reactionscan indicate how various molecules such as metabolites are consumed andproduced through part of all of a life cycle of a biological system.Each reaction thus identifies one or more metabolites that are consumed,one or more metabolites that are produced and, for each consumed andproduced metabolite, a coefficient (which may be set to equal one)indicating a relative amount that is consumed or produced. The reactionmay further include an identification of one or more enzymes, one or mycofactors and/or one or more environmental characteristics that arerequired for the reaction to occur and/or that otherwise affects aprobability of the reaction occurring or a property of the reaction. Thereactions may be identified based on (for example) online or localdigital content (e.g., from one or more scientific papers or databases)and/or results from one or more wet-lab experiments.

At block 615, a stoichiometry matrix is generated using the set ofreactions. Each matrix cell within the matrix can correspond to aparticular metabolite and a particular reaction. The value of the cellmay reflect a coefficient of the particular metabolite within theparticular reaction (as indicated in the reaction) and may be set tozero if it is not involved in the reaction. In some instances, metadatais further generated that indicates, for each of one or more reactions,any enzyme, co-factor and/or environmental condition required for thereaction to occur.

At block 620, one or more constraints are identified for the set ofreactions. In some instances, identifying the constraints may includeidentifying values for one or more parameters. For example, for each ofone or more or all of the set of reactions, a constraint may include aflux lower bound and/or a flux upper bound to limit a flux, a quantityof a consumed or produced metabolite, a kinetic constant, a rate ofproduction or decay of a component such as RNA transcript, an enzymeconcentration or activity, a compartment size, and/or a concentration ofan external metabolite. The constraint(s) may be identified based on(for example) user input, online or local data, one or morecommunications from a wet-lab system, and/or learned from statisticalinference.

At block 625, an objective function is defined for the set of reactions.The objective function may identify what is to be maximized and/or whatis to be minimized while identifying a solution. The objective functionmay (for example) identify a metabolite that is produced by one or morereactions or a combination of metabolites that is produced by one ormore reactions. The combination may identify proportions of themetabolites. However, the objective function can have a number oflimitations and may fail to reflect supply and demand within the othermodules. Thus, in some instances, a limited objective function can beconstructed to include a set of target values for each molecule withinthe metabolic network. The target values can incorporate intrinsic-rateparameters, supply rates of molecules, the consumption rates ofmolecules, and the molecule concentrations into a measurement of targetconcentrations of the molecule given supply, demand, and an “on-hand”concentration of each molecule, which represents the concentration of amolecule immediately available to a reaction pathway. The target valuesmay be calculated and incorporated into the objective function toproduce the limited objective function. This may be in the form ofcalculating an absolute difference between the target value and theproportional flux contribution of each molecule. This may be in the formof scaling the proportional flux contribution of each molecule. This maybe in the form of adding to the proportional flux contribution of eachmolecule. Any other mathematical modification of the proportional fluxcontribution of each molecule that adjusts this value by the targetvalue may be used. The target values may be positive or negative. Forpurposes of unit conversion, so that target values can be included inthe objective function and compared to the flux values, the targetvalues may be constructed as rates.

At block 530, for each metabolite related to the set of reactions, anavailability value is determined. For an initial value, the value may beidentified based on (for example) user input, digital content and/orcommunication from another system. Subsequent values may be retrievedfrom a local or remote data object that maintains centralizedavailability values for the set of metabolites.

At block 635, the availability values, constraints and objectivefunction are used to determine the flux of one, more or all of the setof reactions. The flux(es) may indicate a number of times that each ofone, more or all of the reactions were performed in a simulation inaccordance with the availability values, constraints and objectivefunction. The flux(es) may be determined based on aflux-balance-analysis model. In some instances, the flux(es) may bedetermined based on a sampling of all or part of an input spacerepresenting different flux combinations and scoring each input-spaceusing a scoring function.

At block 640, a centralized availability value of one or moremetabolites is updated based on the determined flux(es). Morespecifically, for each metabolite, a cumulative change in themetabolite's availability may be identified based on the cumulativeconsumption and cumulative production of the metabolite across theflux-adjusted set of reactions. The centralized availability value ofthe metabolite can then be incremented and/or decremented accordingly.

In some instances, at least one the one or more modules defined at block605 are to be associated with a model that does not depend on (forexample) a stoichiometry matrix and/or flux based analysis and/or thatis based on physiological modeling. One or more modules based on one ormore different types of models can also, at each time point, identify achange in metabolite availability values, and such changes can also beused to update a local or remote data object with centralizedavailability values. With respect to each metabolite, updates inavailability values may be summed to identify a total change and/orupdated availability value. In some instances, limits are set withrespect to a maximum change that may be effected across subsequent timesteps and/or a maximum or minimum availability value for a metabolite.

At block 645, availability data is availed to a higher-level model.State vectors can then be updated based on data from multiple modules.

Some or all of blocks 620-645 may be repeated for each of multiplesimulated time points in a simulation. Thus, at each time point,constraints can be updated based on state-vector information (e.g.,representing availability of catalysts), an objective function can bedefined (e.g., which may change across time points based on aconfiguration of a higher level objective), updated metaboliteavailability values can be determined, updated reaction fluxes can beidentified, and further updated availability values can be determined.In some instances, a predefined number of simulated time points are tobe evaluated and/or simulated time points corresponding to a predefinedcumulative time-elapsing period are to be evaluated. In some instances,a subsequent simulated time point is to be evaluated until a predefinedcondition is satisfied. For example, a predefined condition may indicatethat metabolite values for a current simulated time point are the sameor substantially similar as compared to a preceding simulated time pointor a preceding simulated time period.

With regard to a repeated iteration of block 630, it will be appreciatedthat an availability value determined for a given metabolite need not beequal to the corresponding updated availability value from the previousiteration of block 640 and/or the sum of the previously determinedavailability value adjusted by the identified flux pertaining to themetabolite. Rather, a processing of the previous time point with respectone or more other modules may have also resulted in a change in themetabolite availability, and/or a higher level constraint and/orprocessing may influence the availability. Thus, the availability valuefor a given metabolite determined at block 630 for a current time pointmay be equal to the availability value determined at block 630 for apreceding time point plus the cumulative updates to the availabilityvalue across modules, with any limits imposed.

While not shown in process 600, one or more variables can be output(e.g., transmitted to a user device). The variable(s) may include finalvalues (e.g., availability values after all iterations have beenperformed), time-course values, high-level values and/or module-specificvalues. For example, the availability data may include, for each of one,more or all metabolites: an availability value (e.g., a finalavailability value) and/or a time course of the availability value. Insome instances, the availability data is output with referenceavailability data. For example, when part or all of the processingperformed to calculate the availability values was associated with aperturbation, the reference availability data may be associated with anunperturbed state. In some instances, a processed version of theavailability data is output. For example, a comparison of availabilityvalues for particular metabolites across time points may be used togenerate one or more growth metrics (e.g., a growth magnitude or rate),which may be output. Outputting the availability data can include (forexample) locally presenting the availability data and/or transmittingthe availability data to another device.

FIG. 7 shows a process 700 for simulating network activity according toan embodiment of the invention. In some instances, process 700 can be avariation of process 600. Process 700 begins at block 705, at whichreaction stoichiometry of a cell simulation is identified. The reactionstoichiometry can pertain to a simulation of an entire cell or to amodule of the cell. The reaction stoichiometry can represent a set ofreactions. For example, a first reaction can simulate dephosphorylationof a compound (e.g., undecaprenyl) and one or more second reactions cansimulate returning the compound to a phosphorylated state. Each reactionin the set of reactions can identify a set of metabolites. Morespecifically, each reaction in the set of reactions can identify one ormore reactant compounds (e.g., a ligand and/or a substrate) that areconsumed during the reaction and one or more product compounds that areproduced during the reaction.

Further, a reaction may (but need not) include one or more non-consumedcompounds, which may function as a catalyst for the reaction. Forexample, a non-consumed compound may include an enzyme, cofactor orribosome. Exemplary specific non-consumed compounds include: folate,undecaprenyl, nicotinamide adenine dinucleotide (NAD), nicotinamideadenine dinucleotide phosphate (NADP), Flavin adenine dinucleotide(FAD), menaquinone, and coenzyme A (CoA). Because the non-consumedcompound is not consumed, it can be reused across different reactions.In some instances, a subset of the set of reactions identify a cyclethat recycles a non-consumed compound.

Stoichiometry can identify relative quantities between each compound ina given reaction. In some instances, the reaction stoichiometry isreduced to lowest common whole ratios (such that a lowest coefficient ina reaction's stoichiometry representation is one).

In some instances, involvement of a non-consumed compound in a reactionor series of reactions is not represented in the reaction or series ofreactions themselves. Rather, metadata associated with the reaction orseries of reactions may identify the role of the non-consumed compound.

At block 710, one or more constraints for the simulation are defined. Insome instances, the reaction stoichiometry can itself serve asconstraints on simulation solutions, though additional constraints canfurther be applied. The additional constraints may correspond to (forexample) simulated environmental conditions and/or empirical bounds(e.g., on metabolite levels, reaction prominence, and/or changes inmetabolite or reaction levels). Thus, a constraint may be configured torestrict a flux value identified for each of one, more or all reaction.In some instances, the additional constraints are identified based onuser input.

In some instances, a constraint is configured to restrict a flux valueof one or more reactions (or series of reactions) based on a quantity orcount of a metabolite. The metabolite can include a non-consumedcompound, such as a cofactor, enzyme or ribosome. Given that thecompound is not consumed by a given reaction or across a series ofreactions (e.g., when it starts and ends the series as the samecompound), the compound may be repeatedly used. However, a rate at whichit can be repeatedly used and thus a rate at which it can facilitateproducing a product compound can be limited based on a duration of timeduring which it is involved in the reaction or series of reactions(e.g., a sequestration duration). The duration may be identified basedon (for example) user input, using a look-up table, from experimentaldata, etc. Thus, a flux for a given reaction or series of reactions(indicating a number of reactions or series of reactions using thenon-consumed compound that may be performed during a period of time) maybe capped at a quantity of the non-consumed compound indicated as beingpresent in the simulation divided by a sequestration time of thenon-consumed compound in the given reaction or series of reactions.

In some instances, a set of reactions or metadata indicate that thenon-consumed compound is involved in and/or is required for multiplereactions (e.g., such that the non-consumed compound is available in itsinitial state upon completion of each of the multiple reactions) ormultiple series of reactions (e.g., such that each of the non-consumedcompound is available in its initial state upon completion of each ofthe series of reactions) or a combination of at least one reaction andat least one series of reactions. When the non-consumed compound isinvolved in and/or required in a series of reactions, the non-consumedcompound may (but need not) be partly transformed through part of theseries and then return to its initial state (e.g., first becomingdephosphorylated and then phosphorylated or first binding to anothercompound and then becoming unbound).

In these instances, each of the reactions or series of reactions may beassociated with a different sequestration duration and/or a differentflux value. Thus, the constraint may be defined based on one or morecharacteristics of the reuse of the non-consumed compound across cyclesof each of the associated reactions or reaction series. The one or morecharacteristics can include a duration (e.g., sequestration duration)and/or a flux value of each of the associated reactions or reactionseries. For example, an intermediate value may be generated for eachreaction or reaction series (that results in a to-be-reused non-consumedcompound) that is set to equal a product of a sequestration duration andflux of the reaction or reaction series. The constraint can indicatethat a quantity (e.g., number or concentration derived therefrom) of thenon-consumed compound is to be set to be at least equal to a sum of theintermediate values. This sum can be representative of—at maximumefficiency of use of non-consumed compound—a quantity of thenon-consumed compounds that are being “used” by the simulated reactions.Thus, a quantity of the non-consumed compound must be at least equal tothis sum. The duration (e.g., sequestration duration) may identify aper-cycle (or per-iteration) time during which the non-consumed compoundis involved with the reaction or reaction series.

At block 715, an objective function for the simulation is defined. Theobjective function may identify one or more metrics that are to bemaximized and/or minimized when identifying a solution. In someinstances, a metric corresponds to a set of values. For example,defining an objective function so as to indicate that biomass growth isto be maximized can include identifying a particular set of compoundsand relative quantities thereof that are representative of biomasslevels.

At block 720, a solution is identified using linear programming (e.g.,using linear algebra) and the constraints. The solution may be one thatabides by each defined constraint. In some instances, many potentialsolutions abide by all constraints, and thus, the objective function canbe used to identify a single solution to select for the simulation(e.g., one that maximizes a given objective, minimizes a given objectiveor corresponds to a highest/lowest statistic based on objectiveevaluations).

In some instances, the solution is one for which fluxes are balanced, inthat quantities of compounds that are produced by the set of reactionsare equal to quantities of compounds that are consumed by the set ofreactions. When the set of reactions correspond to a model of an entirenetwork, this corresponds to a steady-state solution. When the set ofreactions corresponds to a module of a network and when values aresynthesized across modules between time steps, the solution need notcorrespond to a steady-state solution. In some instances, flux balancingis an objective instead of a constraint, such that balancing fluxes tothe extent possible is one of one or more factors used to identify agiven solution across one or more possible solutions but is not arequirement for identifying a solution.

At block 725, it is determined whether a solution that abides with theconstraint(s) has been identified. If not, process 700 proceeds to block730, at which a result indicates that metabolites are not produced inthe simulation. A whole-cell model may receive an indication of a lackof metabolite production associated with the module and determine howthe cell simulation is to be affected (e.g., nonetheless grow, impairedor inhibited growth, no growth or cell death).

When the linear programming did produce a solution, process 700 proceedsto blocks 735, 740 and 745 (which may be performed concurrently and/orin parallel). At block 735, cofactor production is simulated inaccordance with the solution. Depending on the particular solution,block 735 need not occur. For example, the cofactors used in thereactions may entirely correspond to recycled cofactors (e.g., that wereproduced at previous time steps and/or recycled from previous cycleiterations).

At block 740, production of one or more compounds is simulated inaccordance with the solution. Each of the one or more compounds can beproduced in accordance with at least one of the set of reactions. Eachof at least one of the one or more compounds that are produced mayfunction as a ligand or substrate of another reaction. Thoughphysiologically a given compound may first need to be produced before itcan be consumed by a subsequent reaction, the simulation may simulatethese reactions concurrently or even in reverse order in response toidentifying a solution that indicates that both reactions are to occur.

At block 745, one or more reactions that use the cofactor are simulated.The one or more reactions can be configured to transform the one or morecompounds to one or more product compounds. The one or more compoundsthat are transformed can include compounds that are produced at block740. The cofactor is not consumed during the transformation, in that itis availed for reuse during a subsequent reaction-based transformationafter the product compound(s) are produced for a given iteration.

The potential concurrent or parallel operation of blocks 735-745 andlinear-programming solution identifications indicate how a simulationmay identify a solution that would require more cofactors to support thesolution-identified reactions than actually present in the simulation.Specifically, the concurrent or parallel processing can fail to accountfor order requirements physiologically necessary for reactionperformance. That is, if reactions indicate that a production andconsumption of a given compound would be equal, the compound can bedeemed to be balanced. That is, an initial consumption reaction mayessentially “borrow” the compound from a subsequent production reaction.Thus, even if the compound is never initially produced, flux-balanceanalysis may allow simulated reactions that use the compound to occur ifthe reactions indicate that an amount of the compound that is used isless than or equal to an amount of the compound that is subsequentlyproduced.

It will be appreciated that variations of process 700 are contemplated.For example, rather than defining a constraint that relates a quantityof a non-consumed compound to sequestration durations and fluxes, thisrelationship may be integrated into an objective function. For example,an objective may be defined that indicates that a quantity of anon-consumed compound is to be at least equal to a product ofsequestration duration and a flux of a reaction or series thereof (or asum of these products across multiple reactions, multiple reactionseries or a combination of multiple reactions and one or more reactionsseries if each reaction and/or series involves the non-consumedcompound).

Further, while process 700 corresponds to constraints that pertain to acofactor, another type of non-consumed compound can be alternatively oradditionally constrained. For example, a constraint may relate to anenzyme or ribosome.

FIG. 8 shows a representation of reaction series in which a non-consumedcomponent is used. In this example, the non-consumed component is acofactor undecaprenyl (depicted as “u”). It is used in two series ofreactions: one to produce peptidoglycan (depicted as “p”) and one toproduce the wall teichoic acid (WTA, depicted as “w”). Each ofpeptidoglycan and WTA is a structural component of the cell wall ofStaphylococcus aureus and required for growth. In each of the reactions,undecaprenyl is recycled, such that it can be used in a subsequentreaction series.

Though undecaprenyl is required for the production of each ofpeptidoglycan and WTA, it can only support one reaction series at atime. Thus, if a given undecaprenyl compound is supporting a reactionseries for producing peptidoglycan, in the simulation, it cannotconcurrently support a reaction series for producing WTA. Further, whileFIG. 8 depicts only a single (alternative) pair of series of reactions,multiple iterations of each of the pair may be concurrently occurring.

Physiologically, a total quantity of the undecaprenyl compounds that isused in the simulation across both reaction series cannot exceed a sumof those produced and those recycled across previous iterations of thecycle. Further, the quantity of WTA that is produced cannot exceed thequantity of precursors of WTA that is consumed in the reaction or thequantity of undecaprenyl that is available. Similarly, the quantity ofpeptidoylcan that is produced cannot exceed the quantity of precursorsof peptidoyclan that is consumed in the reaction or the quantity ofundecaprenyl that is available.

FIG. 9 shows a partial representation of physiological states of areaction according to an embodiment of the invention. The representationillustrates that, physiologically, at any point in time, a reactioncycle may be occurring in multiple instances. A degree through which aninstance has progressed through the cycle can vary (at the point intime) across instances. For example, FIG. 9 includes an illustration inwhich each of the reaction series include six discrete reactions. At agiven temporal snapshot (represented by the figure), a state of thereaction series is represented by the bolded line, in that therepresentation indicates that a given instance has performed or isperforming each of the reactions represented along the bolded line. Asillustrated, the state of the reaction series differs across theinstances. Specifically, each reaction series is at a different reactionwithin the series. (While the depicted illustration represents eachinstance as corresponding to a different reaction state, it willappreciated that multiple instances may correspond to a given state.)

In each series, undecaprenyl is not released and availed for a differentreaction until the series is complete. Thus, none of the fiveundecaprenyls associated with the five reaction series can, at therepresented time, support transforming the available precursors ofpeptidoyclan or WTA (as represented by the floating p_(Precursor) andw_(Precursor) representations). FIG. 9 also shows a representation of areaction series to synthesize undecaprenyl. However, as indicated by thebolded elements, this synthesis is not yet complete, such that it hasyet to produce an undecaprenyl that can be used interact with apeptidoyclan precursor or WTA precursor.

This representation illustrates how a flux of one or more reactions canbe constrained by a quantity of a non-consumed compound and how therelationship between the flux and quantity further depends on a speed ofa reaction series. For example, if each of the reaction series wasperformed very quickly, a single non-consumed compound could supportmany reaction series within a time period despite being unable toconcurrently support multiple series.

As noted herein, integrating a core module into a whole-cell modelfacilitates tracking a quantity of non-consumed compounds (based onprior production of the compound). Further the integration canfacilitate tracking availability of non-consumed compounds (based ontime cycles of reactions within a reaction series relative to timesteps). Thus, reactions are not supported by a fictitious limitlesssupply of non-consumed compounds. For example, in the depicted instance,even if multiple peptidoyclan precursors were available, if a statevector indicated that all undecaprenyl were involved in a currentreaction series, a simulation may refrain from initiating anotherpeptidoyclan cycle. If at a next time step, two undecaprenyls wereavailable (one as a result of a completion of a reaction series andanother as a result of a new production), two new simulated reactionseries could be initiated.

FIG. 10 shows examples of dynamics of components of a simulated network.A flux-balance module of the network can be configured to determine, foreach of a set of reactions, a flux that indicates a frequency at whichthe reaction is performed. The set of reactions can represent coremetabolism, membrane synthesis and cell wall synthesis. The fluxes canbe determined by identifying a solution space that includes a set ofpotential solutions that meet each of a set of predefined constraints.Each potential solution can identify a flux value for each of the set ofreactions. In this instance, the set of predefined constraints does notinclude any constraint on non-consumed compounds.

A particular solution is then selected from the solution space using anobjective function that identifies a metric that is to be maximized orminimized. For example, the objective function may be defined toindicate that biomass growth is to be maximized and may identifyrelative availability quantities across multiple metabolites thatcorrespond to a biomass representation. The possible solutions can beidentified using stoichiometry defined for each reaction and linearprogramming. Thus, for each of a set of metabolites, the simulation maycalculate an availability of the metabolite based on extent to which itis being consumed and/or produced by one or more reactions.

The network can further be configured to include multiple other modulesto represent replication, transcription and translation actions.Replication can be simulated using a bulk mass-flow model. Transcriptionand translation can each be simulated using a bulk mass-flow model. Ateach time point, a cross-module data structure can be updated based onresults from each model, such that the module results are synthesized.Each module can then retrieve select values from the cross-module datastructure to use for processing at a next time step.

The left three graphs illustrate availability levels in a simulation ofa wild type of a cell. The right three graphs illustrate availabilitylevels in a simulation of a cell having a knockout of gene NWMN_RS06600.A result of this knock out is that undecaprenyl is not synthesized.Initial values for the simulation nonetheless identified presence ofsome undecaprenyl, though no additional undecaprenyl can be produced.

Each of the graphs show an amount (as a count) of different moleculesover a four-generation simulation run. Each generation is completed whena cell-division event is detected. The top graphs show availability ofundecaprenyl-phosphate (bottom line) and undecaprenyl-diphosphate (topline). Both forms are shown in the graph, as the simulated cell canperform reactions that cause the cofactor to switch between thesestates, even when the knockout is in place to preclude synthesis of thecofactor.

With respect to the wild type, the level of each form of the cofactorgrows to each cell division. With respect to the knockout, theundecaprenyl-phosphate is converted to undecaprenyl-diphosphate at thebeginning of the simulation but then it is diluted out through the nextgenerations. More specifically, the availability ofundecaprenyl-diphosphate drops by 50% after each cell division.

The middle-row and bottom-row graphs show how the availability ofpeptidoglycan and WTA change across the simulation time period. As notedabove, each of these compounds are products of reaction series that useundecaprenyl. As shown, the availability of these products are the sameirrespective of whether the knockout was simulated. This occurs becausethe undecaprenyl is not consumed during the reaction series used toproduce peptidoglycan or WTA.

FIG. 11 shows examples of dynamics of components of a simulated networkwhen constraints on reusable components are used. The configuration ofthe network is the same as the configuration of the network used toproduce the graphs of FIG. 10 except that a constraint is imposed thatindicates that an availability of undecaprenyl must be greater than orequal to a sum of a first product of a sequestration duration of thepeptidoglycan reaction series and the flux of the peptidoglycan reactionseries and a second product of a sequestration duration of the WTAreaction series and the flux of the WTA reaction series.

The top graphs, showing the dynamics of undecaprenyl, are the same asthose shown in FIG. 10 . However, the cycle-product graphs for theknockout differ from the corresponding graphs in FIG. 10 . In theconstraint-integrated simulation, the availability of both thepeptiglycan cycle product and the WTA cycle product decrease overgenerations. More specifically, after each cell division, the cycleproducts drop by half after each cell division, following the pattern ofundecaprenyl diphosphate. Thus, the constraint caused the reducedprevalence of the cofactor in the knockout to also cause a reduction inthe flux of the cofactor-supported reaction series.

Thus, the added constraint improves the accuracy of the simulation.Importantly, the accuracy improvement includes improving the accuracy ofthe interplay between availability of different compounds. Accuratelysimulating this dependency can improve the ability by which thesimulation can accurately estimate the effect of (for example) apharmaceutical, a mutation and/or an environment. Output from thesimulation can be provided to (for example) one or more user devices,drug-screening systems, and/or treatment-provision systems. Thus,improved accuracy of the simulation can improve the quality ofdeveloping and/or selecting effective treatments.

Specific details are given in the above description to provide athorough understanding of the embodiments. However, it is understoodthat the embodiments can be practiced without these specific details.For example, circuits can be shown in block diagrams in order not toobscure the embodiments in unnecessary detail. In other instances,well-known circuits, processes, algorithms, structures, and techniquescan be shown without unnecessary detail in order to avoid obscuring theembodiments.

Implementation of the techniques, blocks, steps and means describedabove can be done in various ways. For example, these techniques,blocks, steps and means can be implemented in hardware, software, or acombination thereof. For a hardware implementation, the processing unitscan be implemented within one or more application specific integratedcircuits (ASICs), digital signal processors (DSPs), digital signalprocessing devices (DSPDs), programmable logic devices (PLDs), fieldprogrammable gate arrays (FPGAs), processors, controllers,micro-controllers, microprocessors, other electronic units designed toperform the functions described above, and/or a combination thereof.

Also, it is noted that the embodiments can be described as a processwhich is depicted as a flowchart, a flow diagram, a data flow diagram, astructure diagram, or a block diagram. Although a flowchart can describethe operations as a sequential process, many of the operations can beperformed in parallel or concurrently. In addition, the order of theoperations can be re-arranged. A process is terminated when itsoperations are completed, but could have additional steps not includedin the figure. A process can correspond to a method, a function, aprocedure, a subroutine, a subprogram, etc. When a process correspondsto a function, its termination corresponds to a return of the functionto the calling function or the main function.

Furthermore, embodiments can be implemented by hardware, software,scripting languages, firmware, middleware, microcode, hardwaredescription languages, and/or any combination thereof. When implementedin software, firmware, middleware, scripting language, and/or microcode,the program code or code segments to perform the necessary tasks can bestored in a machine readable medium such as a storage medium. A codesegment or machine-executable instruction can represent a procedure, afunction, a subprogram, a program, a routine, a subroutine, a module, asoftware package, a script, a class, or any combination of instructions,data structures, and/or program statements. A code segment can becoupled to another code segment or a hardware circuit by passing and/orreceiving information, data, arguments, parameters, and/or memorycontents. Information, arguments, parameters, data, etc. can be passed,forwarded, or transmitted via any suitable means including memorysharing, message passing, ticket passing, network transmission, etc.

For a firmware and/or software implementation, the methodologies can beimplemented with modules (e.g., procedures, functions, and so on) thatperform the functions described herein. Any machine-readable mediumtangibly embodying instructions can be used in implementing themethodologies described herein. For example, software codes can bestored in a memory. Memory can be implemented within the processor orexternal to the processor. As used herein the term “memory” refers toany type of long term, short term, volatile, nonvolatile, or otherstorage medium and is not to be limited to any particular type of memoryor number of memories, or type of media upon which memory is stored.

Moreover, as disclosed herein, the term “storage medium”, “storage” or“memory” can represent one or more memories for storing data, includingread only memory (ROM), random access memory (RAM), magnetic RAM, corememory, magnetic disk storage mediums, optical storage mediums, flashmemory devices and/or other machine readable mediums for storinginformation. The term “machine-readable medium” includes, but is notlimited to portable or fixed storage devices, optical storage devices,wireless channels, and/or various other storage mediums capable ofstoring that contain or carry instruction(s) and/or data.

While the principles of the disclosure have been described above inconnection with specific apparatuses and methods, it is to be clearlyunderstood that this description is made only by way of example and notas limitation on the scope of the disclosure.

What is claimed is:
 1. A system for using a simulator to generate metabolite time course data comprising: one or more data processors; and a non-transitory computer readable storage medium containing instructions which, when executed on the one or more data processors, cause the one or more data processors to perform actions including: defining one or more modules within a biological system based on corresponding biological functions; defining a set of reactions for the one or more modules within the biological system, wherein the set of reactions indicate how various molecules are consumed and produced through at least a portion of a life cycle of the biological system, and wherein each reaction of the set of reactions identifies stoichiometry indicative of one or more metabolites that are consumed, one or more metabolites that are produced and, for each consumed and produced metabolite, a coefficient indicating a relative amount that is consumed or produced; identifying one or more additional constraints for the set of reactions; defining an objective function for the set of reactions based on the stoichiometries of the set of reactions; and executing a simulation using the set of reactions, the one or more additional constraints, and the objective function to generate the metabolite time course data for a given time point.
 2. The system of claim 1, wherein the actions further include: determining an availability value for each metabolite related to the set of reactions, wherein executing the simulation includes determining, for each reaction of the set of reactions, a flux of the reaction based on the availability values, the one or more additional constraints, and the objective function; and updating a centralized availability value for each metabolite based on the identified fluxes.
 3. The system of claim 2, wherein the fluxes indicate a number of times that each reaction of the set of reactions were performed in the simulation in accordance with the availability values, the one or more additional constraints, and the objective function.
 4. The system of claim 1, wherein the set of reactions further identify one or more enzymes, one or more cofactors, one or more characteristics that are required for a reaction to occur, one or more characteristics that affects a probability of the reaction occurring, one or more properties of the reaction, or any combination thereof.
 5. The system of claim 1, wherein the one or more additional constraints include a flux lower bound and/or a flux upper bound to limit a flux, a quantity of a consumed or produced metabolite, a kinetic constant, a rate of production or decay of a component, an enzyme concentration or activity, a compartment size, a concentration of an external metabolite, or any combination thereof.
 6. The system of claim 1, wherein the actions further include, for a subsequent time point: identifying one or more additional constraints for the set of reactions; defining an objective function for the set of reactions based on the stoichiometries of the set of reactions; and executing a simulation using the set of reactions, the one or more additional constraints, and the objective function to generate the metabolite time course data for the subsequent time point.
 7. The system of claim 1, wherein the objective function identifies one or more metrics that are to be maximized and/or minimized when identifying a solution.
 8. A computer-implemented method comprising: defining one or more modules within a biological system based on corresponding biological functions; defining a set of reactions for the one or more modules within the biological system, wherein the set of reactions indicate how various molecules are consumed and produced through at least a portion of a life cycle of the biological system, and wherein each reaction of the set of reactions identifies stoichiometry indicative of one or more metabolites that are consumed, one or more metabolites that are produced and, for each consumed and produced metabolite, a coefficient indicating a relative amount that is consumed or produced; identifying one or more additional constraints for the set of reactions; defining an objective function for the set of reactions based on the stoichiometries of the set of reactions; and executing a simulation using the set of reactions, the one or more additional constraints, and the objective function to generate the metabolite time course data for a given time point.
 9. The computer-implemented method of claim 8, further comprising: determining an availability value for each metabolite related to the set of reactions, wherein executing the simulation includes determining, for each reaction of the set of reactions, a flux of the reaction based on the availability values, the one or more additional constraints, and the objective function; and updating a centralized availability value for each metabolite based on the identified fluxes.
 10. The computer-implemented method of claim 9, wherein the fluxes indicate a number of times that each reaction of the set of reactions were performed in the simulation in accordance with the availability values, the one or more additional constraints, and the objective function.
 11. The computer-implemented method of claim 8, wherein the set of reactions further identify one or more enzymes, one or more cofactors, one or more characteristics that are required for a reaction to occur, one or more characteristics that affects a probability of the reaction occurring, one or more properties of the reaction, or any combination thereof.
 12. The computer-implemented method of claim 8, wherein the one or more additional constraints include a flux lower bound and/or a flux upper bound to limit a flux, a quantity of a consumed or produced metabolite, a kinetic constant, a rate of production or decay of a component, an enzyme concentration or activity, a compartment size, a concentration of an external metabolite, or any combination thereof.
 13. The computer-implemented method of claim 8, further comprising, for a subsequent time point: identifying one or more additional constraints for the set of reactions; defining an objective function for the set of reactions based on the stoichiometries of the set of reactions; and executing a simulation using the set of reactions, the one or more additional constraints, and the objective function to generate the metabolite time course data for the subsequent time point.
 14. The computer-implemented method of claim 8, wherein the objective function identifies one or more metrics that are to be maximized and/or minimized when identifying a solution.
 15. A computer-program product tangibly embodied in a non-transitory machine-readable storage medium, including instructions configured to cause one or more data processors to perform actions including: defining one or more modules within a biological system based on corresponding biological functions; defining a set of reactions for the one or more modules within the biological system, wherein the set of reactions indicate how various molecules are consumed and produced through at least a portion of a life cycle of the biological system, and wherein each reaction of the set of reactions identifies stoichiometry indicative of one or more metabolites that are consumed, one or more metabolites that are produced and, for each consumed and produced metabolite, a coefficient indicating a relative amount that is consumed or produced; identifying one or more additional constraints for the set of reactions; defining an objective function for the set of reactions based on the stoichiometries of the set of reactions; and executing a simulation using the set of reactions, the one or more additional constraints, and the objective function to generate the metabolite time course data for a given time point.
 16. The computer-program product of claim 15, wherein the actions further include: determining an availability value for each metabolite related to the set of reactions, wherein executing the simulation includes determining, for each reaction of the set of reactions, a flux of the reaction based on the availability values, the one or more additional constraints, and the objective function; and updating a centralized availability value for each metabolite based on the identified fluxes.
 17. The computer-program product of claim 16, wherein the fluxes indicate a number of times that each reaction of the set of reactions were performed in the simulation in accordance with the availability values, the one or more additional constraints, and the objective function.
 18. The computer-program product of claim 15, wherein the set of reactions further identify one or more enzymes, one or more cofactors, one or more characteristics that are required for a reaction to occur, one or more characteristics that affects a probability of the reaction occurring, one or more properties of the reaction, or any combination thereof.
 19. The computer-program product of claim 15, wherein the one or more additional constraints include a flux lower bound and/or a flux upper bound to limit a flux, a quantity of a consumed or produced metabolite, a kinetic constant, a rate of production or decay of a component, an enzyme concentration or activity, a compartment size, a concentration of an external metabolite, or any combination thereof.
 20. The computer-program product of claim 15, wherein the actions further include, for a subsequent time point: identifying one or more additional constraints for the set of reactions; defining an objective function for the set of reactions based on the stoichiometries of the set of reactions; and executing a simulation using the set of reactions, the one or more additional constraints, and the objective function to generate the metabolite time course data for the subsequent time point. 